This invention relates to semiconductor devices, and is particularly concerned with trench devices, i.e., devices in which at least one electrode is set into the wall or bottom or forms part of a trench or recess below a major, usually planar, surface of a semiconductor device. The use of trenches is particularly advantageous for devices such as IGBT's (insulated gate bipolar transistors) which are capable of operating at high power and voltage levels. The limit on the upper value of voltage at which such devices can be used is determined by the breakdown voltage of a device. For a device which is capable of operating at high power and at high voltage levels, it is important that the device has a low on-state resistance and turns-off (i.e., current flow through the device ceases) promptly and reliably in response to a turn-off signal. It has proved difficult to produce such a device which reliably meets the conflicting requirements of high current, high voltage operation and a safe, reliable current control characteristic.